A medical valve connector comprising a tubular body having an inlet fitting of the male luer or luer-lock type with an inner tubular element displaceable axially from a retracted position for closing a passage of flow towards an outlet fitting to an advanced position for opening said passage of flow. A tubular body made of elastic material, set between the inlet and outlet fittings, tends to keep the inner tubular element in the retracted position. Also the outlet fitting can rotate and axially translate between a retracted position and an advanced position.